(dy)/(dx)=xsqrt(y)cos(x)

Lösung

\frac{d y}{d x} = x y cos (x)

y = \frac{c _{1} x sin ( x )}{2} + \frac{x ^{2} sin ^{2} ( x )}{4} + \frac{x cos ( x ) sin ( x )}{2} + \frac{c _{1} cos ( x )}{2} + \frac{cos ^{2} ( x )}{4} + \frac{c _{1}^{2}}{4}

Schritte zur Lösung

\frac{d y}{d x} = x y cos (x)

Solve separable ODE:

y = \frac{c _{1} x sin ( x )}{2} + \frac{x ^{2} sin ^{2} ( x )}{4} + \frac{x cos ( x ) sin ( x )}{2} + \frac{c _{1} cos ( x )}{2} + \frac{cos ^{2} ( x )}{4} + \frac{c _{1}^{2}}{4}

y = \frac{c _{1} x sin ( x )}{2} + \frac{x ^{2} sin ^{2} ( x )}{4} + \frac{x cos ( x ) sin ( x )}{2} + \frac{c _{1} cos ( x )}{2} + \frac{cos ^{2} ( x )}{4} + \frac{c _{1}^{2}}{4}

(\frac{d y}{d t}) - (\frac{3}{t}) \cdot y = 2 t^{3} e^{2 t}, y (1) = 0

d er i v a t i v e f (x) = 7 x^{2} + 6 x

t an g e n t - 2 x^{2}, at x = - 2

in v erse l a pl a ce \frac{12}{s ^{2} - 5}

d er i v a t i v e 1 - 4 x