Internal problem ID [4862]
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]]
\[ \boxed {x^{2} y^{\prime \prime }+y^{\prime } \left (1+x \right )-y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= 1+x \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)
\[ y \left (x \right ) = \left (\frac {c_{1} \left (x +1\right ) {\mathrm e}^{-\frac {1}{x}}}{x}+c_{2} \right ) {\mathrm e}^{\frac {1}{x}} x \]
✓ Solution by Mathematica
Time used: 0.077 (sec). Leaf size: 21
DSolve[x^2*y''[x]+(x+1)*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{\frac {1}{x}} x+c_2 (x+1) \]