15.22.5 problem 5

Internal problem ID [3339]
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 : 5
Date solved : Monday, January 27, 2025 at 07:34:31 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} y^{\prime }&=\ln \left (y x \right ) \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: 0.002 (sec). Leaf size: 14

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

\[ y \left (x \right ) = 1+\frac {1}{2} \left (x -1\right )^{2}+\frac {1}{12} \left (x -1\right )^{4}+\operatorname {O}\left (\left (x -1\right )^{5}\right ) \]

✓ Solution by Mathematica

Time used: 0.023 (sec). Leaf size: 23

AsymptoticDSolveValue[{D[y[x],x]==Log[x*y[x]],{y[1]==1}},y[x],{x,1,"5"-1}]
 

\[ y(x)\to \frac {1}{12} (x-1)^4+\frac {1}{2} (x-1)^2+1 \]