solve the 1st order homogeneous differential equation

$2t{w}'-3w=0$

WORKED ANSWER

For a 1st order homogeneous ODE, have solution formula:

$A\cdot e^{-\int p}$

So we are doing the following integration

$e^{-\int \frac{3}{2t}}\cdot A$

$\Rightarrow \int 3\cdot \frac{1}{t}\cdot \frac{1}{2}dt$

$\Rightarrow \int \frac{3}{2}\cdot \frac{1}{t}dt$

$\Rightarrow \frac{3}2\cdot \ln t$

Now we've done the integration, sub-in to the original solution formula. Using laws of logarithms:

$A\cdot e^{\ln t^{-\frac{3}{2}}}$

$\Rightarrow A\cdot t\cdot -\frac{3}{2}$

PROBLEM

The actual solution given is:

$c\cdot t^{\frac{3}{2}}$

So you can see the solution and worked answer different by -1.

Any help please guys?

$2t{w}'-3w=0$

WORKED ANSWER

For a 1st order homogeneous ODE, have solution formula:

$A\cdot e^{-\int p}$

So we are doing the following integration

$e^{-\int \frac{3}{2t}}\cdot A$

$\Rightarrow \int 3\cdot \frac{1}{t}\cdot \frac{1}{2}dt$

$\Rightarrow \int \frac{3}{2}\cdot \frac{1}{t}dt$

$\Rightarrow \frac{3}2\cdot \ln t$

Now we've done the integration, sub-in to the original solution formula. Using laws of logarithms:

$A\cdot e^{\ln t^{-\frac{3}{2}}}$

$\Rightarrow A\cdot t\cdot -\frac{3}{2}$

PROBLEM

The actual solution given is:

$c\cdot t^{\frac{3}{2}}$

So you can see the solution and worked answer different by -1.

Any help please guys?

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