Internal problem ID [14831]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Chapter 4 review exercises, page 219
Problem number: 10.
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)]`]]
\[ \boxed {\left (1+t \right )^{2} y^{\prime \prime }-2 y^{\prime } \left (1+t \right )+2 y=0} \] Given that one solution of the ode is \begin {align*} y_1 &= 1+t \end {align*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 15
dsolve([(t+1)^2*diff(y(t),t$2)-2*(t+1)*diff(y(t),t)+2*y(t)=0,t+1],singsol=all)
\[ y \left (t \right ) = \left (t +1\right ) \left (c_{1} +c_{2} \left (t +1\right )\right ) \]
✓ Solution by Mathematica
Time used: 0.028 (sec). Leaf size: 18
DSolve[(t+1)^2*y''[t]-2*(t+1)*y'[t]+2*y[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to (t+1) (c_2 (t+1)+c_1) \]