71.1.153 problem 180 (page 297)

Internal problem ID [19329]
Book : V.V. Stepanov, A course of differential equations (in Russian), GIFML. Moscow (1958)
Section : All content
Problem number : 180 (page 297)
Date solved : Thursday, October 02, 2025 at 04:18:55 PM
CAS classification : [NONE]

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

With initial conditions

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

✗ Maple

ode:=diff(diff(y(x),x),x) = x+y(x)^2; 
ic:=[y(0) = 0, D(y)(0) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],{x,2}]==y[x]^2+x; 
ic={y[0]==0,Derivative[1][y][0] == 1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - y(x)**2 + Derivative(y(x), (x, 2)),0) 
ics = {y(0): 0, Subs(Derivative(y(x), x), x, 0): 1} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : solve: Cannot solve -x - y(x)**2 + Derivative(y(x), (x, 2))