83.35.14 problem 14

Internal problem ID [19434]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter VII. Exact differential equations and certain particular forms of equations. Misc. Exercise on chapter VII. Page 118
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 01:42:50 PM
CAS classification : [[_3rd_order, _fully, _exact, _linear]]

\begin{align*} \left (x^{3}-4 x \right ) y^{\prime \prime \prime }+\left (9 x^{2}-4\right ) y^{\prime \prime }+18 x y^{\prime }+6 y&=6 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 44

dsolve((x^3-4*x)*diff(y(x),x$3)+(9*x^2-4)*diff(y(x),x$2)+18*x*diff(y(x),x)+6*y(x)=6,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {8 \ln \left (x \right ) c_{1} x +x^{4}-c_{1} x^{3}+\left (c_{2} -12\right ) x^{2}+c_3 x +4 c_{2}}{\left (x +2\right )^{2} \left (x -2\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.224 (sec). Leaf size: 83

DSolve[(x^3-4*x)*D[y[x],{x,3}]+(9*x^2-4)*D[y[x],{x,2}]+18*x*D[y[x],x]+6*y[x]==6,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {6 x^4-3 c_3 x^3+2 (-24+c_1-c_2+3 c_3) x^2-2 (2 c_1-5 c_2+18 c_3) x+24 c_3 x \log (x)+8 (12+c_1-c_2+3 c_3)}{6 \left (x^2-4\right )^2} \]