75.2.4 problem 24

Internal problem ID [16681]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 2. The method of isoclines. Exercises page 27
Problem number : 24
Date solved : Tuesday, January 28, 2025 at 09:17:52 AM
CAS classification : [[_linear, `class A`]]

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

✓ Solution by Maple

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

dsolve(diff(y(x),x)=1/2*(x-2*y(x)+3),y(x), singsol=all)
 

\[ y = \frac {x}{2}+1+c_{1} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 20

DSolve[D[y[x],x]==1/2*(x-2*y[x]+3),y[x],x,IncludeSingularSolutions -> True]
 

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