75.3.3 problem 43

Internal problem ID [16700]
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 : 43
Date solved : Tuesday, January 28, 2025 at 09:18:39 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 13

dsolve([diff(y(x),x)=x+y(x),y(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.050 (sec). Leaf size: 15

DSolve[{D[y[x],x]==x+y[x],{y[0]==1}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -x+2 e^x-1 \]