83.27.7 problem 7

Internal problem ID [19353]
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. Exercise VII (A) at page 104
Problem number : 7
Date solved : Tuesday, January 28, 2025 at 01:35:13 PM
CAS classification : [[_2nd_order, _exact, _linear, _homogeneous]]

\begin{align*} \left (x^{2}-x \right ) y^{\prime \prime }+2 \left (2 x +1\right ) y^{\prime }+2 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 41

dsolve((x^2-x)*diff(y(x),x$2)+2*(2*x+1)*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {12 \ln \left (x \right ) c_{1} x^{3}+\left (-3 x^{4}+18 x^{2}-6 x +1\right ) c_{1} +c_{2} x^{3}}{\left (x -1\right )^{5}} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 52

DSolve[(x^2-x)*D[y[x],{x,2}]+2*(2*x+1)*D[y[x],x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {-3 c_2 x^4-3 c_1 x^3+12 c_2 x^3 \log (x)+18 c_2 x^2-6 c_2 x+c_2}{3 (x-1)^5} \]