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Beliebt Rechnen >

ty^{''}-y^'=t^2+t,y(1)=1,y^'(1)=5

Lösung

t y^{^{''}} - y^{^{'}} = t^{2} + t, y (1) = 1, y^{^{'}} (1) = 5

Lösung

y = (\frac{13}{12} + \frac{11}{12}) t^{2} - \frac{13}{12} + \frac{4 t ^{3} + 6 t ^{2} ln ( t ) - 3 t ^{2}}{12}

Schritte zur Lösung

t y^{''} (t) - y^{'} (t) = t^{2} + t

Solve linear ODE:

y = (\frac{13}{12} + \frac{11}{12}) t^{2} - \frac{13}{12} + \frac{4 t ^{3} + 6 t ^{2} ln ( t ) - 3 t ^{2}}{12}

y = (\frac{13}{12} + \frac{11}{12}) t^{2} - \frac{13}{12} + \frac{4 t ^{3} + 6 t ^{2} ln ( t ) - 3 t ^{2}}{12}

Graph

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