75.12.10 problem 284

Internal problem ID [16876]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 284
Date solved : Tuesday, January 28, 2025 at 09:38:45 AM
CAS classification : [_quadrature]

\begin{align*} x^{2}+x y^{\prime }&=3 x +y^{\prime } \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 20

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

\[ y = -\frac {x^{2}}{2}+2 x +2 \ln \left (x -1\right )+c_{1} \]

✓ Solution by Mathematica

Time used: 0.025 (sec). Leaf size: 29

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

\[ y(x)\to \int _1^x-\frac {(K[1]-3) K[1]}{K[1]-1}dK[1]+c_1 \]