What is the rigorous justification for treating differentials as fractions while solving differential equations?
7474
What am I doing when I separate the variables of a differential equation?
158794
Transforming Differential Equation to a Kummer's Equation
20280
Proving that expression is equivalent to the definition of derivative
155177
How do you write a differential operator as a matrix?
31845
When not to treat dy/dx as a fraction in single-variable calculus?
115712
Application of Derivatives rigorous proof
154080
circular reasoning in proving $\frac{\sin x}x\to1,x\to0$
41720
Getting equation from differential equations
148498
Specific system of differential equations
44366
ODE $\frac{dy}{dx}=x^{2}+y^{2}, y(0)=0.$
3360
Is $\frac{\textrm{d}y}{\textrm{d}x}$ not a ratio?
30695
Can I solve this differential equation at a point?
35526
What's the proper way to typeset a differential operator?
71465
solution of $y' = \exp \left(-\frac yx\right) + \frac yx$
134122
When is differentiating an equation valid?
49984
Valid justification for algebraic manipulation of $\mathrm{d}y/\mathrm{d}x$?
55888
Why my differential equations become True?