Internal problem ID [8569]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 1, linear first order
Problem number: 233.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_homogeneous, `class D`], _Bernoulli]
\[ \boxed {y^{\prime } x y-y^{2}=-a \,x^{3} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 30
dsolve(x*y(x)*diff(y(x),x)-y(x)^2+a*x^3*cos(x)=0,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: 0.351 (sec). Leaf size: 38
DSolve[x*y[x]*y'[x]-y[x]^2+a*x^3*Cos[x]==0,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*}