35.7.24 problem 29

Internal problem ID [6206]
Book : Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley. 2006
Section : Chapter 8, Ordinary differential equations. Section 7. Other second-Order equations. page 435
Problem number : 29
Date solved : Monday, January 27, 2025 at 01:47:42 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+\left (1+x \right ) y^{\prime }-y&=0 \end{align*}

Using reduction of order method given that one solution is

\begin{align*} y&=1+x \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 16

dsolve([x^2*diff(y(x),x$2)+(x+1)*diff(y(x),x)-y(x)=0,x+1],singsol=all)
 

\[ y = c_{2} x \,{\mathrm e}^{\frac {1}{x}}+c_{1} x +c_{1} \]

✓ Solution by Mathematica

Time used: 0.097 (sec). Leaf size: 26

DSolve[x^2*D[y[x],{x,2}]+(x+1)*D[y[x],x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 e^{\frac {1}{x}-1} x+e^2 c_2 (x+1) \]