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Popular >

y^{''}-4y^'+3y=(x^2-3x)e^x

Solution

y^{^{''}} - 4 y^{^{'}} + 3 y = (x^{2} - 3 x) e^{x}

Solution

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{e ^{x} x ^{3}}{6} + \frac{e ^{x} x ^{2}}{2} + \frac{e ^{x} x}{2}

Solution steps

y^{''} (x) - 4 y^{'} (x) + 3 y = (x^{2} - 3 x) e^{x}

Solve linear ODE:

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{e ^{x} x ^{3}}{6} + \frac{e ^{x} x ^{2}}{2} + \frac{e ^{x} x}{2}

y = c_{1} e^{3 x} + c_{2} e^{x} - \frac{e ^{x} x ^{3}}{6} + \frac{e ^{x} x ^{2}}{2} + \frac{e ^{x} x}{2}

Graph

Popular Examples

y^{''}+4y^'+3y=50x*sin(x)

y^{^{''}} + 4 y^{^{'}} + 3 y = 50 x \cdot sin (x)

y^{''}+y^'-2y=(2+6x)e^x

y^{^{''}} + y^{^{'}} - 2 y = (2 + 6 x) e^{x}

y^{''}-2y^'+y=(e^x)/((x^2+1))

y^{^{''}} - 2 y^{^{'}} + y = \frac{e ^{x}}{( x ^{2} + 1 )}

y^{''}+y=9cos(2x)

y^{^{''}} + y = 9 cos (2 x)

y^{''}-12y^'+36y=24x+2

y^{^{''}} - 12 y^{^{'}} + 36 y = 24 x + 2

Frequently Asked Questions (FAQ)

What is the solution for y^{''}-4y^'+3y=(x^2-3x)e^x ?
The solution for y^{''}-4y^'+3y=(x^2-3x)e^x is y=c_{1}e^{3x}+c_{2}e^x-(e^xx^3)/6+(e^xx^2)/2+(e^xx)/2