7.24 problem 29

Internal problem ID [4354]

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.
ODE order: 2.
ODE degree: 1.

CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]

Solve \begin {gather*} \boxed {x^{2} y^{\prime \prime }+\left (x +1\right ) y^{\prime }-y=0} \end {gather*} Given that one solution of the ode is \begin {align*} y_1 &= x +1 \end {align*}

Solution by Maple

Time used: 0.0 (sec). Leaf size: 26

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

\[ y \relax (x ) = \left (\frac {c_{1} \left (x +1\right ) {\mathrm e}^{-\frac {1}{x}}}{x}+c_{2}\right ) {\mathrm e}^{\frac {1}{x}} x \]

Solution by Mathematica

Time used: 0.053 (sec). Leaf size: 21

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

\begin{align*} y(x)\to c_1 e^{\frac {1}{x}} x+c_2 (x+1) \\ \end{align*}