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Popular >

y^{''}-y=x-1

Solution

y^{^{''}} - y = x - 1

Solution

y = c_{1} e^{x} + c_{2} e^{- x} - x + 1

Solution steps

y^{''} (x) - y = x - 1

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- x} - x + 1

y = c_{1} e^{x} + c_{2} e^{- x} - x + 1

Popular Examples

y^{''}+4y=t^2+8e^t,y(0)=0,y^'(0)=7

y^{^{''}} + 4 y = t^{2} + 8 e^{t}, y (0) = 0, y^{^{'}} (0) = 7

x^{''}+10x^'+16x=10sin(4t)

x^{^{''}} + 10 x^{^{'}} + 16 x = 10 sin (4 t)

y^{''}-4y=e^xcos(x),y(0)=0.9,y^'(0)=-1.5

y^{^{''}} - 4 y = e^{x} cos (x), y (0) = 0.9, y^{^{'}} (0) = - 1.5

(d^2y)/(dx^2)+y=3sin(2x)

\frac{d ^{2} y}{d x ^{2}} + y = 3 sin (2 x)

y^{''}-4y=e^xcos(x),y(0)=0.9,y^'(0)=-1.1

y^{^{''}} - 4 y = e^{x} cos (x), y (0) = 0.9, y^{^{'}} (0) = - 1.1

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-y=x-1 ?
The solution for y^{''}-y=x-1 is y=c_{1}e^x+c_{2}e^{-x}-x+1