Internal problem ID [5436]
Internal file name [OUTPUT/4927_Tuesday_February_06_2024_10_14_22_PM_63877284/index.tex]
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.
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.
\[ \boxed {\left (2 x -3\right ) y^{\prime \prime \prime }-\left (6 x -7\right ) y^{\prime \prime }+4 y^{\prime } x -4 y=8} \] Unable to solve this ODE.
\[ \begin {array}{lll} & {} & \textrm {Let's solve}\hspace {3pt} \\ {} & {} & \left (2 x -3\right ) \left (\frac {d}{d x}y^{\prime \prime }\right )-\left (6 x -7\right ) \left (\frac {d}{d x}y^{\prime }\right )+4 y^{\prime } x -4 y=8 \\ \bullet & {} & \textrm {Highest derivative means the order of the ODE is}\hspace {3pt} 3 \\ {} & {} & \frac {d}{d x}y^{\prime \prime } \end {array} \]
Maple trace
`Methods for third order ODEs: --- Trying classification methods --- trying a quadrature trying high order exact linear fully integrable trying differential order: 3; linear nonhomogeneous with symmetry [0,1] trying high order linear exact nonhomogeneous trying differential order: 3; missing the dependent variable checking if the LODE is of Euler type Equation is the LCLM of -1/x*y(x)+diff(y(x),x), -y(x)+diff(y(x),x), -2*y(x)+diff(y(x),x) trying differential order: 1; missing the dependent variable checking if the LODE is of Euler type <- LODE of Euler type successful Euler equation successful trying differential order: 1; missing the dependent variable checking if the LODE has constant coefficients <- constant coefficients successful trying differential order: 1; missing the dependent variable checking if the LODE has constant coefficients <- constant coefficients successful <- solving the LCLM ode successful `
✓ Solution by Maple
Time used: 0.016 (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)
\[ y \left (x \right ) = -2+c_{1} x +{\mathrm e}^{x} c_{2} +c_{3} {\mathrm e}^{2 x} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 26
DSolve[(2*x-3)*y'''[x]-(6*x-7)*y''[x]+4*x*y'[x]-4*y[x]==8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 x+c_2 e^x-c_3 e^{2 x}-2 \]