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Popular >

y^{''}+y=2x

Solution

y^{^{''}} + y = 2 x

Solution

y = c_{1} cos (x) + c_{2} sin (x) + 2 x

Solution steps

y^{''} (x) + y = 2 x

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + 2 x

y = c_{1} cos (x) + c_{2} sin (x) + 2 x

Graph

Popular Examples

y^{''}-y^'=te^t,y(0)=2,y^'(0)=1

y^{^{''}} - y^{^{'}} = t e^{t}, y (0) = 2, y^{^{'}} (0) = 1

y^{''}+3y^'+2y=e^t

y^{^{''}} + 3 y^{^{'}} + 2 y = e^{t}

y^{''}-y=xsin(x)

y^{^{''}} - y = x sin (x)

y^{''}+4y=-12sin(2x)

y^{^{''}} + 4 y = - 12 sin (2 x)

y^{'''}-4y^{''}=x+xe^{4x}

y^{^{'''}} - 4 y^{^{''}} = x + x e^{4 x}

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+y=2x ?
The solution for y^{''}+y=2x is y=c_{1}cos(x)+c_{2}sin(x)+2x