Does this method make sense written down this way?

[studentxlol]

Homework Statement

Solve the differential equation: $$\frac{d^2y}{dx^2}=3x^2-10x+3$$

The Attempt at a Solution

$$\int\int \frac{d}{dx}\frac({dy}{dx})3x^2-10x+3=\frac{1}{4}x^4-\frac{5}{3}x^3+\frac{3}{2}x^2+c$$

Does that make sense mathematically?

 

[SammyS]

Homework Statement

Solve the differential equation: $$\frac{d^2y}{dx^2}=3x^2-10x+3$$

The Attempt at a Solution

$$\int\int \frac{d}{dx}(\frac{dy}{dx})3x^2-10x+3=\frac{1}{4}x^4-\frac{5}{3}x^3+\frac{3}{2}x^2+c$$

Does that make sense mathematically?
...

No. Not even if you fix the parentheses.

$\displaystyle\int\frac{d}{dx}\left(\frac{dy}{dx} \right)dx=\int\left(3x^2-10x+3\right)dx$

$\displaystyle\frac{dy}{dx}=x^3-5x^2+3x+C_1$

So that: $\displaystyle y=\int\left\{\int\frac{d}{dx}\left( \frac{dy}{dx} \right)dx\right\}dx=\int\left(x^3-5x^2+3x+C_1\right)dx$

which has an additional constant of integration.​