Internal problem ID [15055]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Section 6. Linear equations of the first order. The Bernoulli equation. Exercises page
54
Problem number: 162.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_Bernoulli]
\[ \boxed {2 y^{\prime } \ln \left (x \right )+\frac {y}{x}-\frac {\cos \left (x \right )}{y}=0} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 36
dsolve(2*diff(y(x),x)*ln(x)+y(x)/x=cos(x)/y(x),y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {\sqrt {\ln \left (x \right ) \left (\sin \left (x \right )+c_{1} \right )}}{\ln \left (x \right )} \\ y \left (x \right ) &= -\frac {\sqrt {\ln \left (x \right ) \left (\sin \left (x \right )+c_{1} \right )}}{\ln \left (x \right )} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.311 (sec). Leaf size: 42
DSolve[2*y'[x]*Log[x]+y[x]/x==Cos[x]/y[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {\sqrt {\sin (x)+c_1}}{\sqrt {\log (x)}} \\ y(x)\to \frac {\sqrt {\sin (x)+c_1}}{\sqrt {\log (x)}} \\ \end{align*}