Internal problem ID [1262]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 7 Series Solutions of Linear Second Equations. 7.3 SERIES SOLUTIONS NEAR AN
ORDINARY POINT II. Exercises 7.3. Page 338
Problem number: 24.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (2 x +3\right ) y^{\prime \prime }+3 y^{\prime }-y x=0} \end {gather*} With initial conditions \begin {align*} [y \left (-1\right ) = 2, y^{\prime }\left (-1\right ) = -3] \end {align*}
With the expansion point for the power series method at \(x = -1\).
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 20
Order:=6; dsolve([(3+2*x)*diff(y(x),x$2)+3*diff(y(x),x)-x*y(x)=0,y(-1) = 2, D(y)(-1) = -3],y(x),type='series',x=-1);
\[ y \relax (x ) = 2-3 \left (x +1\right )+\frac {7}{2} \left (x +1\right )^{2}-5 \left (x +1\right )^{3}+\frac {197}{24} \left (x +1\right )^{4}-\frac {287}{20} \left (x +1\right )^{5}+\mathrm {O}\left (\left (x +1\right )^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 44
AsymptoticDSolveValue[{(3+2*x)*y''[x]+3*y'[x]-x*y[x]==0,{y[-1]==2,y'[-1]==-3}},y[x],{x,-1,5}]
\[ y(x)\to -\frac {287}{20} (x+1)^5+\frac {197}{24} (x+1)^4-5 (x+1)^3+\frac {7}{2} (x+1)^2-3 (x+1)+2 \]