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Popular >

(4-t^2)y^'+2ty=3t^2

Solution

(4 - t^{2}) y^{^{'}} + 2 t y = 3 t^{2}

Solution

y = - \frac{3}{2} ln (t + 2) + \frac{3}{8} t^{2} ln (t + 2) - \frac{3}{t + 2} + \frac{3 t ^{2}}{4 ( t + 2 )} + \frac{3}{2} ln (t - 2) - \frac{3}{8} t^{2} ln (t - 2) - \frac{3}{t - 2} + \frac{3 t ^{2}}{4 ( t - 2 )} + 4 c_{1} - c_{1} t^{2}

Solution steps

(4 - t^{2}) y^{'} (t) + 2 t y = 3 t^{2}

Solve linear ODE:

y = - \frac{3}{2} ln (t + 2) + \frac{3}{8} t^{2} ln (t + 2) - \frac{3}{t + 2} + \frac{3 t ^{2}}{4 ( t + 2 )} + \frac{3}{2} ln (t - 2) - \frac{3}{8} t^{2} ln (t - 2) - \frac{3}{t - 2} + \frac{3 t ^{2}}{4 ( t - 2 )} + 4 c_{1} - c_{1} t^{2}

y = - \frac{3}{2} ln (t + 2) + \frac{3}{8} t^{2} ln (t + 2) - \frac{3}{t + 2} + \frac{3 t ^{2}}{4 ( t + 2 )} + \frac{3}{2} ln (t - 2) - \frac{3}{8} t^{2} ln (t - 2) - \frac{3}{t - 2} + \frac{3 t ^{2}}{4 ( t - 2 )} + 4 c_{1} - c_{1} t^{2}

Popular Examples

integral of 1/2 t^2

\int \frac{1}{2} t^{2} d t

(\partial)/(\partial x)(xe^y+ye^{-x})

\frac{\partial}{\partial x} (x e^{y} + y e^{- x})

integral of (5x+7y)

\int (5 x + 7 y) d x

area f(x)=2sin(x)+x,-pi,pi area

f (x) = 2 sin (x) + x, - π, π

(2/((1-x)^3))^'

(\frac{2}{( 1 - x ) ^{3}})^{^{'}}

Frequently Asked Questions (FAQ)

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