Is there a way to derive the second linearly independent solution to ODE whose characteristic quadratic has double roots?
11654
Where does $xe^x$ solution come from when the characteristic polynomial is square?
128355
Does $e^{tx} + x = t - 1$ yield a solution/s to $\frac{dx}{dt} = \frac{e^{-tx} - x}{e^{-tx} + t}$?
30723
Second derivative "formula derivation"
126235
Why does DSolve return two solutions for my ODE?
158893
Separable Differential Equation
14656
The differential equation $xu_{x}+yu_{y}=2u$ satisfying the initial condition $y=xg(x),u=f(x)$
96022
Symmetry of second derivative - Sufficiency of twice-differentiability
104489
Derivative (or differential) of symmetric square root of a matrix
153816
Real Roots and Differentiation
137330
Solving two parametric ODEs and then plotting a curve derived from the solutions with respect to the parameter
38003
Can we differentiate equations without changing the solutions?
20444
Derive quadratic formula
67158
Solve $y'-\int_0^xy(t)dt=2$
129454
Solution to a quadratic form
148498
Specific system of differential equations
139419
Problem on the domain of the solution of a differential equation
30697
Solution of a Riccati ODE