75.6.29 problem 162

Internal problem ID [16785]
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
Date solved : Tuesday, January 28, 2025 at 09:22:42 AM
CAS classification : [_Bernoulli]

\begin{align*} 2 y^{\prime } \ln \left (x \right )+\frac {y}{x}&=\frac {\cos \left (x \right )}{y} \end{align*}

✓ Solution by Maple

Time used: 0.122 (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 &= \frac {\sqrt {\ln \left (x \right ) \left (\sin \left (x \right )+c_{1} \right )}}{\ln \left (x \right )} \\ y &= -\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: 0.345 (sec). Leaf size: 70

DSolve[2*D[y[x],x]*Log[x]+y[x]/x==Cos[x]/y[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {\sqrt {2 \int _1^x\frac {1}{2} \cos (K[1])dK[1]+c_1}}{\sqrt {\log (x)}} \\ y(x)\to \frac {\sqrt {2 \int _1^x\frac {1}{2} \cos (K[1])dK[1]+c_1}}{\sqrt {\log (x)}} \\ \end{align*}