Mathematicsforum Q&A

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1 answer 67 views

Solve $y + \frac{d}{{dx}}(xy) = x(\sin x + \log x)$.

answered Dec 4, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 58 views

Find the differential equation of system of concentric circles with centre (1,2).

answered Dec 4, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 47 views

Solve the differential equation $\left( {1 + {y^2}} \right){\tan ^{ - 1}}xdx + 2y\left( {1 + {x^2}} \right)dy = 0$.

answered Dec 4, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 45 views

Form the differential equation by eliminating $A$ and $B$ in $A{x^2} + B{y^2} = 1$.

answered Dec 4, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 22 views

Solve the differential equation $dy = \cos x(2 - y{\mathop{\rm cosec}\nolimits} x)dx$ given that $y = 2,$ when $x = \frac{\pi }{2}$

answered Dec 4, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 39 views

Solve $2(y + 3) - xy\frac{{dy}}{{dx}} = 0,$ given that $y(1) = - 2$.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 34 views

Solve $(x + y)(dx - dy) = dx + dy$.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 41 views

Find the general solution of ${y^2}dx + \left( {{x^2} - xy + {y^2}} \right)dy = 0$.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 41 views

Find the general solution of the differential equation $\left( {1 + {y^2}} \right) + \left( {x - {e^{{{\tan }^{ - 1}}y}}} \right)\frac{{dy}}{{dx}} = 0$.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 36 views

Solve ${x^2}\frac{{dy}}{{dx}} = {x^2} + xy + {y^2}$.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 47 views

Find the equation of a curve passing through origin and satisfying the differential equation $\left( {1 + {x^2}} \right)\frac{{dy}}{{dx}} + 2xy = 4{x^2}$.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 45 views

Form the differential equation of all circles which pass through origin and whose centres lie on Y-axis.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 35 views

Form the differential equation having $y = {\left( {{{\sin }^{ - 1}}x} \right)^2} + A{\cos ^{ - 1}}x + B$, where $A$ and $B$ are arbitrary constants, as its general solution.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 21 views

If $y(t)$ is a solution of $(1 + t)\frac{{dy}}{{dt}} - ty = 1$ and $y(0) = - 1,$ then show that $y(1) = - \frac{1}{2}$.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 34 views

If $y(x)$ is a solution of $\left( {\frac{{2 + \sin x}}{{1 + y}}} \right)\frac{{dy}}{{dx}} = - \cos x$ and $y(0) = 1,$ then find the value of $y\left( {\frac{\pi }{2}} \right)$.

answered Nov 22, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 37 views

Find the general solution of $\left( {x + 2{y^3}} \right)\frac{{dy}}{{dx}} = y$.

answered Nov 21, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 55 views

Solve the differential equation $\frac{{dy}}{{dx}} = 1 + x + {y^2} + x{y^2},$ when $y = 0$ and $x = 0$.

answered Nov 21, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 53 views

Solve $ydx - xdy = {x^2}ydx$.

answered Nov 21, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 36 views

Solve the differential equation $\frac{{dy}}{{dx}} + 1 = {e^{x + y}}$.

answered Nov 21, 2022 in Differential Equation by sachin (38.8k points)

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1 answer 46 views

Find the general solution of $\frac{{dy}}{{dx}} + ay = {e^{mx}}$.

answered Nov 21, 2022 in Differential Equation by sachin (38.8k points)

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