60.4.55 problem 1503

Internal problem ID [11506]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 3, linear third order
Problem number : 1503
Date solved : Monday, January 27, 2025 at 11:22:46 PM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} \left (x^{2}+1\right ) y^{\prime \prime \prime }+8 x y^{\prime \prime }+10 y^{\prime }-3+\frac {1}{x^{2}}-2 \ln \left (x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 67

dsolve((x^2+1)*diff(diff(diff(y(x),x),x),x)+8*x*diff(diff(y(x),x),x)+10*diff(y(x),x)-3+1/x^2-2*ln(x)=0,y(x), singsol=all)
 

\[ y = \frac {\left (45 x^{5}+150 x^{3}+225 x \right ) \ln \left (x \right )-9 x^{5}+225 c_{1} x^{4}+\left (225 c_{2} -50\right ) x^{3}+450 c_{1} x^{2}+\left (675 c_{2} -225\right ) x +225 c_3}{225 \left (x^{2}+1\right )^{2}} \]

✓ Solution by Mathematica

Time used: 0.568 (sec). Leaf size: 258

DSolve[-3 + x^(-2) - 2*Log[x] + 10*D[y[x],x] + 8*x*D[y[x],{x,2}] + (1 + x^2)*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{225} \left (-3 (17+75 c_2) \arctan (x)-\frac {51 x}{x^2+1}-\frac {34 x}{\left (x^2+1\right )^2}-\frac {225 c_2 x}{x^2+1}-\frac {150 c_2 x}{\left (x^2+1\right )^2}-\frac {225 c_1}{4 \left (x^2+1\right )^2}-9 x+\frac {47}{x-i}+\frac {47}{x+i}+45 x \log (x)+60 i \log (-x+i)+\frac {171}{2} i \log (1-i x)-\frac {171}{2} i \log (1+i x)+\frac {30 \log (x)}{x-i}+\frac {30 \log (x)}{x+i}-\frac {30 i \log (x)}{(x-i)^2}+\frac {30 i \log (x)}{(x+i)^2}-60 i \log (x+i)+\frac {75 c_2}{x-i}+\frac {75 c_2}{x+i}+\frac {225}{2} i c_2 \log (1-i x)-\frac {225}{2} i c_2 \log (1+i x)\right )+c_3 \]