75.6.8 problem 132

Internal problem ID [16764]
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 : 132
Date solved : Tuesday, January 28, 2025 at 09:21:46 AM
CAS classification : [_linear]

\begin{align*} y^{\prime } x \ln \left (x \right )-y&=3 x^{3} \ln \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 12

dsolve(diff(y(x),x)*x*ln(x)-y(x)=3*x^3*(ln(x))^2,y(x), singsol=all)
 

\[ y = \left (x^{3}+c_{1} \right ) \ln \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.039 (sec). Leaf size: 14

DSolve[D[y[x],x]*x*Log[x]-y[x]==3*x^3*(Log[x])^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^3+c_1\right ) \log (x) \]