15.22.4 problem 4

Internal problem ID [3338]
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 : 4
Date solved : Monday, January 27, 2025 at 07:34:30 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=3 x +\frac {y}{x} \end{align*}

Using series method with expansion around

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

With initial conditions

\begin{align*} y \left (1\right )&=3 \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 9

Order:=5; 
dsolve([diff(y(x),x)=3*x+y(x)/x,y(1) = 3],y(x),type='series',x=1);
 

\[ y \left (x \right ) = 3 x^{2} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 17

AsymptoticDSolveValue[{D[y[x],x]==3*x+y[x]/x,{y[1]==3}},y[x],{x,1,"5"-1}]
 

\[ y(x)\to 3 (x-1)^2+6 (x-1)+3 \]