Internal problem ID [6484]
Book: Own collection of miscellaneous problems
Section: section 4.0
Problem number: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {\left (1+x \right ) \left (3 x -1\right ) y^{\prime \prime }+y^{\prime } \cos \relax (x )-3 x y=0} \end {gather*} With the expansion point for the power series method at \(x = 0\).
✓ Solution by Maple
Time used: 0.004 (sec). Leaf size: 49
Order:=6; dsolve((x+1)*(3*x-1)*diff(y(x),x$2)+cos(x)*diff(y(x),x)-3*x*y(x)=0,y(x),type='series',x=0);
\[ y \relax (x ) = \left (1-\frac {1}{2} x^{3}-\frac {5}{8} x^{4}-\frac {53}{40} x^{5}\right ) y \relax (0)+\left (x +\frac {1}{2} x^{2}+\frac {1}{2} x^{3}+\frac {7}{12} x^{4}+\frac {7}{6} x^{5}\right ) D\relax (y )\relax (0)+O\left (x^{6}\right ) \]
✓ Solution by Mathematica
Time used: 0.001 (sec). Leaf size: 63
AsymptoticDSolveValue[(x+1)*(3*x-1)*y''[x]+Cos[x]*y'[x]-3*x*y[x]==0,y[x],{x,0,5}]
\[ y(x)\to c_1 \left (-\frac {53 x^5}{40}-\frac {5 x^4}{8}-\frac {x^3}{2}+1\right )+c_2 \left (\frac {7 x^5}{6}+\frac {7 x^4}{12}+\frac {x^3}{2}+\frac {x^2}{2}+x\right ) \]