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Popular >

y^{''}-3y^'+2y=(x^2+x)e^{3x}

Solution

y^{^{''}} - 3 y^{^{'}} + 2 y = (x^{2} + x) e^{3 x}

Solution

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{e ^{3 x} x ^{2}}{2} - e^{3 x} x + e^{3 x}

Solution steps

y^{''} (x) - 3 y^{'} (x) + 2 y = (x^{2} + x) e^{3 x}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{e ^{3 x} x ^{2}}{2} - e^{3 x} x + e^{3 x}

y = c_{1} e^{2 x} + c_{2} e^{x} + \frac{e ^{3 x} x ^{2}}{2} - e^{3 x} x + e^{3 x}

Graph

Popular Examples

y^{''}+2y^'+y=e^{3x},y(0)=0,y^'(0)=0

y^{^{''}} + 2 y^{^{'}} + y = e^{3 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{''}-4y^'+3y=9x^2

y^{^{''}} - 4 y^{^{'}} + 3 y = 9 x^{2}

y^{''}+6y^'-7y=21x^2-8x-30

y^{^{''}} + 6 y^{^{'}} - 7 y = 21 x^{2} - 8 x - 30

y^{''}+y^'-2y=e^{-2*x}sin(x)

y^{^{''}} + y^{^{'}} - 2 y = e^{- 2 \cdot x} sin (x)

y^{''}-2y^'-3y=6x+4,y(0)=1,y^'(0)=-3

y^{^{''}} - 2 y^{^{'}} - 3 y = 6 x + 4, y (0) = 1, y^{^{'}} (0) = - 3

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-3y^'+2y=(x^2+x)e^{3x} ?
The solution for y^{''}-3y^'+2y=(x^2+x)e^{3x} is y=c_{1}e^{2x}+c_{2}e^x+(e^{3x}x^2)/2-e^{3x}x+e^{3x}