75.3.2 problem 42

Internal problem ID [16699]
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 : 42
Date solved : Tuesday, January 28, 2025 at 09:18:23 AM
CAS classification : [[_Riccati, _special]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.092 (sec). Leaf size: 35

dsolve([diff(y(x),x)=x+y(x)^2,y(0) = 0],y(x), singsol=all)
 

\[ y = \frac {\sqrt {3}\, \operatorname {AiryAi}\left (1, -x \right )+\operatorname {AiryBi}\left (1, -x \right )}{\sqrt {3}\, \operatorname {AiryAi}\left (-x \right )+\operatorname {AiryBi}\left (-x \right )} \]

✓ Solution by Mathematica

Time used: 1.158 (sec). Leaf size: 80

DSolve[{D[y[x],x]==x+y[x]^2,{y[0]==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {x^{3/2} \operatorname {BesselJ}\left (-\frac {4}{3},\frac {2 x^{3/2}}{3}\right )-x^{3/2} \operatorname {BesselJ}\left (\frac {2}{3},\frac {2 x^{3/2}}{3}\right )+\operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )}{2 x \operatorname {BesselJ}\left (-\frac {1}{3},\frac {2 x^{3/2}}{3}\right )} \]