15.22.3 problem 3

Internal problem ID [3337]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 40, page 186
Problem number : 3
Date solved : Monday, January 27, 2025 at 07:34:29 AM
CAS classification : [_separable]

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

Using series method with expansion around

\begin{align*} 1 \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 5

Order:=5; 
dsolve([diff(y(x),x)=x^2*y(x)^2,y(1) = 0],y(x),type='series',x=1);
 

\[ y \left (x \right ) = 0 \]

✓ Solution by Mathematica

Time used: 0.022 (sec). Leaf size: 4

AsymptoticDSolveValue[{D[y[x],x]==x^2*y[x]^2,{y[1]==0}},y[x],{x,1,"5"-1}]
 

\[ y(x)\to 0 \]