75.7.17 problem 192

Internal problem ID [16810]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 7, Total differential equations. The integrating factor. Exercises page 61
Problem number : 192
Date solved : Tuesday, January 28, 2025 at 09:33:26 AM
CAS classification : [_linear]

\begin{align*} 2 x^{2} y+2 y+5+\left (2 x^{3}+2 x \right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 14

dsolve(( 2*x^2*y(x)+2*y(x)+5)+(2*x^3+2*x)*diff(y(x),x)=0,y(x), singsol=all)
 

\[ y = \frac {-\frac {5 \arctan \left (x \right )}{2}+c_{1}}{x} \]

✓ Solution by Mathematica

Time used: 0.041 (sec). Leaf size: 31

DSolve[( 2*x^2*y[x]+2*y[x]+5)+(2*x^3+2*x)*D[y[x],x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {\int _1^x-\frac {5}{2 \left (K[1]^2+1\right )}dK[1]+c_1}{x} \]