Internal problem ID [14790]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 4. Higher Order Equations. Exercises 4.8, page 203
Problem number: 14.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (-2 x +3\right ) y^{\prime \prime }+2 y^{\prime }-2 y=0} \] With initial conditions \begin {align*} [y \left (0\right ) = 3, y^{\prime }\left (0\right ) = -2] \end {align*}
With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([(3-2*x)*diff(y(x),x$2)+2*diff(y(x),x)-2*y(x)=0,y(0) = 3, D(y)(0) = -2],y(x),type='series',x=0);
\[ y \left (x \right ) = 3-2 x +\frac {5}{3} x^{2}-\frac {2}{9} x^{3}+\frac {1}{18} x^{4}+\frac {1}{135} x^{5}+\operatorname {O}\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 36
AsymptoticDSolveValue[{(3-2*x)*y''[x]+2*y'[x]-2*y[x]==0,{y[0]==3,y'[0]==-2}},y[x],{x,0,5}]
\[ y(x)\to \frac {x^5}{135}+\frac {x^4}{18}-\frac {2 x^3}{9}+\frac {5 x^2}{3}-2 x+3 \]