Internal problem ID [13568]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 15. General solutions to Homogeneous linear differential equations. Additional
exercises page 294
Problem number: 15.2 (i).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type
[[_2nd_order, _with_linear_symmetries], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]
\[ \boxed {\left (x +1\right )^{2} y^{\prime \prime }-2 \left (x +1\right ) y^{\prime }+2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 0, y^{\prime }\left (0\right ) = 4] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 13
dsolve([(x+1)^2*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+2*y(x)=0,y(0) = 0, D(y)(0) = 4],y(x), singsol=all)
\[ y \left (x \right ) = 4 x^{2}+4 x \]
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 11
DSolve[{(x+1)^2*y''[x]-2*(x+1)*y'[x]+2*y[x]==0,{y[0]==0,y'[0]==4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to 4 x (x+1) \]