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Popular >

y^{''}+3y^'-4y=10e^x-250cos(3x)

Solution

y^{^{''}} + 3 y^{^{'}} - 4 y = 10 e^{x} - 250 cos (3 x)

Solution

y = c_{1} e^{x} + c_{2} e^{- 4 x} + 2 x e^{x} - 9 sin (3 x) + 13 cos (3 x)

Solution steps

y^{''} (x) + 3 y^{'} (x) - 4 y = 10 e^{x} - 250 cos (3 x)

Solve linear ODE:

y = c_{1} e^{x} + c_{2} e^{- 4 x} + 2 x e^{x} - 9 sin (3 x) + 13 cos (3 x)

y = c_{1} e^{x} + c_{2} e^{- 4 x} + 2 x e^{x} - 9 sin (3 x) + 13 cos (3 x)

Graph

Popular Examples

sum from n=1 to infinity of (4^n)/(n^4)

n = 1 \sum \infty \frac{4 ^{n}}{n ^{4}}

(dx)/(dt)=-3x(1/10 e^{-2t}),x(0)= 4/5

\frac{d x}{d t} = - 3 x (\frac{1}{10} e^{- 2 t}), x (0) = \frac{4}{5}

(\partial)/(\partial y)(-3x^2+7xy-4y^2+x+y)

\frac{\partial}{\partial y} (- 3 x^{2} + 7 x y - 4 y^{2} + x + y)

xy^2y^'=y^3-5x^3,y(1)=6

x y^{2} y^{^{'}} = y^{3} - 5 x^{3}, y (1) = 6

integral of 1/2 e^{2t}

\int \frac{1}{2} e^{2 t} d t

Frequently Asked Questions (FAQ)

What is the solution for y^{''}+3y^'-4y=10e^x-250cos(3x) ?
The solution for y^{''}+3y^'-4y=10e^x-250cos(3x) is y=c_{1}e^x+c_{2}e^{-4x}+2xe^x-9sin(3x)+13cos(3x)