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 Aug29 comment inverse laplace transform - with symbolic variables What is a TU ?. Aug29 comment Partial Fraction decomposition when denominator is in $x^2 + a$ form I tried solving it, by plugging in values - ended up with 4 equations which should give the answer once solved. But it looked tedious and messy so I thought my solution is incorrect... but apparently not. Aug29 comment Partial Fraction decomposition when denominator is in $x^2 + a$ form how did you solve the constants so quickly Aug29 comment Partial Fraction decomposition when denominator is in $x^2 + a$ form which one, the As+B/s^2 + 1 .. is right? May1 comment Differential Equation: Modifying Particular Solution Yes, but I the question here is just asking for the "form" of the particular solution. May1 comment Inverse Laplace transform of $(2s+1)/(s^2 - 4s + 5)$ Thank you so much. May1 comment Finding fundamental set of solution of higher order differential equation Sorry, I don't quite understand why I don't need to use Wronskian to conclude this. In which case then do I need to use the Wronskian to conclude that something is a fundamental set of solution? Thank you May1 comment Differential equation: finding particular solution when the RHS is in form A/t How to know when I need to apply the method of variation of parameter? Apr3 comment Why is the particular solution of $y'' - 4y' +3y = e^t$ not in the form of $Ae^t$ "both $e^t$ and $te^t$" meaning the homogenous equation looks like $Ay'' - By' + Cy = e^t + te^t$, then the particular solution will look like $t^2e^t$, am I correct? Apr3 comment Why is the particular solution of $y'' - 4y' +3y = e^t$ not in the form of $Ae^t$ and if $te^t$ is already in the homogeneous solution, we will need to multiply by one more $t$ making it $t^2e^t$? Apr1 comment Particular Solution of $y'' - 3y' - 4y = 3e^{2t}$ Thank you. I feel ashamed that I did not see this. Mar31 comment Differential Equation $y'' + 8y' - 9y = 0$ and Wronskian yes. thank you. Feb18 comment Differential Equation $y'' - 4y' + 4y = 0$ Then in what case will it has a form of $Ce^tcos(t)...Ce^tsin(t)$ Feb17 comment Differential Equation $y'' - 4y' + 4y = 0$ is it considered to have "repeated roots" if the roots are (r-2)(r+2)? (roots of 2 and -2). No right? Feb17 comment Differential Equation $(2x^2 + y^2)\,dx - xy \, dy = 0$ In most problem (that I've seen so far) that are homogeneous, you set $u =\frac{y}{x}$ , if I set $u =\frac{x}{y}$ would that be a problem or would it just give you the same thing? Feb17 comment Differential Equation $(2x^2 + y^2)\,dx - xy \, dy = 0$ Now I have,$$y' = \frac{2x^2 + y^2}{xy}$$ $$yy' = 2x + \frac{y^2}{x}$$ Jan25 comment Differential Equation: Using substitution $u(x)=y+x$, solve $\frac{dy}{dx} = (y+x)^2$ what if $u(x) = y^3$. what would be $\frac{dy}{dx}$ in this case. Jan25 comment Differential Equation: Using substitution $u(x)=y+x$, solve $\frac{dy}{dx} = (y+x)^2$ thank you! I see i now Jan25 comment Differential Equation $y' = \frac{ty(4-y)}{(1+y)}$ i feel kinda stupid after knowing that. Dec11 comment Partial differentiation dz/ds when function of z is differentiable function of x and y but not given explicitly Indeed. Thank you.