Internal problem ID [3761]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 18
Problem number: 509.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Bernoulli]
\[ \boxed {y y^{\prime } x -y^{2}=a \,x^{3} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(x*y(x)*diff(y(x),x) = a*x^3*cos(x)+y(x)^2,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \sqrt {2 \sin \left (x \right ) a +c_{1}}\, x y \left (x \right ) = -\sqrt {2 \sin \left (x \right ) a +c_{1}}\, x \end{align*}
✓ Solution by Mathematica
Time used: 0.377 (sec). Leaf size: 38
DSolve[x y[x] y'[x]==a x^3 Cos[x]+y[x]^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -x \sqrt {2 a \sin (x)+c_1} y(x)\to x \sqrt {2 a \sin (x)+c_1} \end{align*}