75.3.5 problem 45

Internal problem ID [16702]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 3. The method of successive approximation. Exercises page 31
Problem number : 45
Date solved : Tuesday, January 28, 2025 at 09:18:42 AM
CAS classification : [_linear]

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

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 9

dsolve([x*diff(y(x),x)=2*x-y(x),y(1) = 2],y(x), singsol=all)
 

\[ y = x +\frac {1}{x} \]

✓ Solution by Mathematica

Time used: 0.026 (sec). Leaf size: 10

DSolve[{x*D[y[x],x]==2*x-y[x],{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

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