75.12.13 problem 287

Internal problem ID [16879]
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 : 287
Date solved : Tuesday, January 28, 2025 at 09:39:15 AM
CAS classification : [_linear]

\begin{align*} \left (2 x -1\right ) y^{\prime }-2 y&=\frac {1-4 x}{x^{2}} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 15

dsolve((2*x-1)*diff(y(x),x)-2*y(x)=(1-4*x)/x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 18

DSolve[(2*x-1)*D[y[x],x]-2*y[x]==(1-4*x)/x^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{x}+2 c_1 x-c_1 \]