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Beliebt Rechnen >

y^{''}-y^'=e^2x,y(0)=0,y(1)=0

Lösung

y^{^{''}} - y^{^{'}} = e^{2} x, y (0) = 0, y (1) = 0

Lösung

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

Schritte zur Lösung

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

Solve linear ODE:

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

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

Graph

Beliebte Beispiele

y^{''}-4y=sin(x)

y^{^{''}} - 4 y = sin (x)

(D^2+D)y=-cos(x)

(D^{2} + D) y = - cos (x)

4y^{''}+2y^'+70y=4cos(4t)

4 y^{^{''}} + 2 y^{^{'}} + 70 y = 4 cos (4 t)

y^{''''}-2y^{''}-8y=6e^{2x}

y^{^{''''}} - 2 y^{^{''}} - 8 y = 6 e^{2 x}

y^{''}-5y^'+6y=pix^2+3

y^{^{''}} - 5 y^{^{'}} + 6 y = π x^{2} + 3