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Beliebt Rechnen >

4y^{''}-8y^'=cos(2x)+7x^2

Lösung

4 y^{^{''}} - 8 y^{^{'}} = cos (2 x) + 7 x^{2}

Lösung

y = c_{1} e^{2 x} + c_{2} - \frac{1}{32} sin (2 x) - \frac{1}{32} cos (2 x) - \frac{7 x ^{3}}{24} + \frac{- 7 x ^{2} - 7 x}{16}

Schritte zur Lösung

4 y^{''} (x) - 8 y^{'} (x) = cos (2 x) + 7 x^{2}

Solve linear ODE:

y = c_{1} e^{2 x} + c_{2} - \frac{1}{32} sin (2 x) - \frac{1}{32} cos (2 x) - \frac{7 x ^{3}}{24} + \frac{- 7 x ^{2} - 7 x}{16}

y = c_{1} e^{2 x} + c_{2} - \frac{1}{32} sin (2 x) - \frac{1}{32} cos (2 x) - \frac{7 x ^{3}}{24} + \frac{- 7 x ^{2} - 7 x}{16}

Graph

Beliebte Beispiele

y^{''}-2y^'+y=(4e^x)/(x^2+1)

y^{^{''}} - 2 y^{^{'}} + y = \frac{4 e ^{x}}{x ^{2} + 1}

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

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

(d^2y)/(dx^2)+y=csc(x)cot(x)

\frac{d ^{2} y}{d x ^{2}} + y = csc (x) cot (x)

y^{''}-4y^'+3=e^{-5x},y(0)=0,y^'(0)=0

y^{^{''}} - 4 y^{^{'}} + 3 = e^{- 5 x}, y (0) = 0, y^{^{'}} (0) = 0

y^{''}-4y^'+13y=5cos(2x)

y^{^{''}} - 4 y^{^{'}} + 13 y = 5 cos (2 x)