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Beliebt Rechnen >

(d^2y)/(dx^2)+y=e^x

Lösung

\frac{d ^{2} y}{d x ^{2}} + y = e^{x}

Lösung

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{x}

Schritte zur Lösung

\frac{d ^{2} y}{d x ^{2}} + y = e^{x}

Solve linear ODE:

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{x}

y = c_{1} cos (x) + c_{2} sin (x) + \frac{1}{2} e^{x}

Graph

Beliebte Beispiele

0.1x^{''}+10x=100sin(ct)

0.1 x^{^{''}} + 10 x = 100 sin (c t)

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

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

y^{''}-3y^'+2y=e^{3t},y(0)=-1,y^'(0)=-4

y^{^{''}} - 3 y^{^{'}} + 2 y = e^{3 t}, y (0) = - 1, y^{^{'}} (0) = - 4

y^{''}+a^2y^'=cos(bx)

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

y^{''}-5y^'+4y=2x^2

y^{^{''}} - 5 y^{^{'}} + 4 y = 2 x^{2}