40.14.8 problem 29

Internal problem ID [6779]
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
Date solved : Tuesday, January 28, 2025 at 03:10:32 PM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} \left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 x y^{\prime }-4 y&=8 \end{align*}

✓ Solution by Maple

Time used: 0.010 (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)
 

\[ y = -2+c_1 x +{\mathrm e}^{x} c_2 +c_3 \,{\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.236 (sec). Leaf size: 26

DSolve[(2*x-3)*D[y[x],{x,3}]-(6*x-7)*D[y[x],{x,2}]+4*x*D[y[x],x]-4*y[x]==8,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_1 x+c_2 e^x-c_3 e^{2 x}-2 \]