What is the solution for ty^'=y-5t^2sin(3t),y(pi/3)=0 ?

The solution for ty^'=y-5t^2sin(3t),y(pi/3)=0 is y=(5tcos(3t))/3+(5t)/3

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ty^'=y-5t^2sin(3t),y(pi/3)=0

t y^{^{'}} = y - 5 t^{2} sin (3 t), y (\frac{π}{3}) = 0

y = \frac{5 t cos ( 3 t )}{3} + \frac{5 t}{3}

Solution steps

t y^{'} (t) = y - 5 t^{2} sin (3 t)

Solve linear ODE:

y = \frac{5 t cos ( 3 t )}{3} + \frac{5 t}{3}

y = \frac{5 t cos ( 3 t )}{3} + \frac{5 t}{3}

\frac{\partial}{\partial x} (e^{2 x} sin (y))

x \to 0 lim (cot (5 x))

\frac{\partial}{\partial x} (2 y + 3 y sin (x))

\frac{d}{d x} (arcsin (\frac{x}{1 + x ^{2}}))

\int \frac{z ^{4} + 10 z ^{2} + 25}{z ^{3} + 5 z} d z

What is the solution for ty^'=y-5t^2sin(3t),y(pi/3)=0 ?
The solution for ty^'=y-5t^2sin(3t),y(pi/3)=0 is y=(5tcos(3t))/3+(5t)/3