Internal problem ID [9839]
Internal file name [OUTPUT/8784_Monday_June_06_2022_05_27_37_AM_81891150/index.tex]
Book: Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section: Chapter 3, linear third order
Problem number: 1515.
ODE order: 3.
ODE degree: 1.
The type(s) of ODE detected by this program : "unknown"
Maple gives the following as the ode type
[[_3rd_order, _with_linear_symmetries]]
Unable to solve or complete the solution.
\[ \boxed {y^{\prime \prime \prime } x^{3}+3 \left (1-a \right ) x^{2} y^{\prime \prime }+\left (4 b^{2} c^{2} x^{1+2 c}+1-4 \nu ^{2} c^{2}+3 a \left (-1+a \right ) x \right ) y^{\prime }+\left (4 b^{2} c^{2} \left (-a +c \right ) x^{2 c}+a \left (4 \nu ^{2} c^{2}-a^{2}\right )\right ) y=0} \] Unable to solve this ODE.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & y^{\prime \prime \prime } x^{3}+3 \left (1-a \right ) x^{2} y^{\prime \prime }+\left (4 b^{2} c^{2} x^{1+2 c}+1-4 \nu ^{2} c^{2}+3 a \left (-1+a \right ) x \right ) y^{\prime }+\left (4 b^{2} c^{2} \left (-a +c \right ) x^{2 c}+a \left (4 \nu ^{2} c^{2}-a^{2}\right )\right ) y=0 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 3 \\ {} & {} & y^{\prime \prime \prime } \end {array} \]
✗ Solution by Maple
dsolve(x^3*diff(diff(diff(y(x),x),x),x)+3*(1-a)*x^2*diff(diff(y(x),x),x)+(4*b^2*c^2*x^(2*c+1)+1-4*nu^2*c^2+3*a*(a-1)*x)*diff(y(x),x)+(4*b^2*c^2*(c-a)*x^(2*c)+a*(4*c^2*nu^2-a^2))*y(x)=0,y(x), singsol=all)
\[ \text {No solution found} \]
✗ Solution by Mathematica
Time used: 0.0 (sec). Leaf size: 0
DSolve[(a*(-a^2 + 4*c^2*nu^2) + 4*b^2*c^2*(-a + c)*x^(2*c))*y[x] + (1 - 4*c^2*nu^2 + 3*(-1 + a)*a*x + 4*b^2*c^2*x^(1 + 2*c))*y'[x] + 3*(1 - a)*x^2*y''[x] + x^3*Derivative[3][y][x] == 0,y[x],x,IncludeSingularSolutions -> True]
Not solved