Internal problem ID [5436]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 19. Linear equations with variable coefficients (Misc. types). Supplemetary
problems. Page 132
Problem number: 29.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y=8} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 19
dsolve((2*x-3)*diff(y(x),x$3)-(6*x-7)*diff(y(x),x$2)+4*x*diff(y(x),x)-4*y(x)=8,y(x), singsol=all)
\[ y = -2+c_{1} x +c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 26
DSolve[(2*x-3)*y'''[x]-(6*x-7)*y''[x]+4*x*y'[x]-4*y[x]==8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x+c_2 e^x-c_3 e^{2 x}-2 \]