15.22.6 problem 6

Internal problem ID [3340]
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 : 6
Date solved : Monday, January 27, 2025 at 07:34:32 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=1+y^{2} \end{align*}

Using series method with expansion around

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 18

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

\[ y \left (x \right ) = -1+2 \left (x -1\right )-2 \left (x -1\right )^{2}+\frac {8}{3} \left (x -1\right )^{3}-\frac {10}{3} \left (x -1\right )^{4}+\operatorname {O}\left (\left (x -1\right )^{5}\right ) \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 35

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

\[ y(x)\to -\frac {10}{3} (x-1)^4+\frac {8}{3} (x-1)^3-2 (x-1)^2+2 (x-1)-1 \]