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Beliebt Rechnen >

t^2y^{''}-3ty^'+4y=t^2*ln(t)

Lösung

t^{2} y^{^{''}} - 3 t y^{^{'}} + 4 y = t^{2} \cdot ln (t)

Lösung

y = c_{1} t^{2} + c_{2} ln (t) t^{2} + \frac{t ^{2} ln ^{3} ( t )}{6}

Schritte zur Lösung

t^{2} y^{''} (t) - 3 t y^{'} (t) + 4 y = t^{2} \cdot ln (t)

Solve linear ODE:

y = c_{1} t^{2} + c_{2} ln (t) t^{2} + \frac{t ^{2} ln ^{3} ( t )}{6}

y = c_{1} t^{2} + c_{2} ln (t) t^{2} + \frac{t ^{2} ln ^{3} ( t )}{6}

Graph

Beliebte Beispiele

limit as x approaches 0 of x^6ln(x)

x \to 0 lim (x^{6} ln (x))

integral of 1/((4+x^2))

\int \frac{1}{( 4 + x ^{2} )} d x

derivative f(x)=(3x)/x ,x=8

d er i v a t i v e f (x) = \frac{3 x}{x}, x = 8

y^'+6y=60,y(1)=90

y^{^{'}} + 6 y = 60, y (1) = 90

integral of 1/(sqrt(25x^2-64))

\int \frac{1}{25 x ^{2} - 64} d x