Find the general solution of the differential equation: y' + 3x^2 y = 0

The general solution of the differential equation y' + 3x^2 y = 0 is:

Step-by-step explanation:

This equation its a Separable First Order Differential Equation, this means that you can express the equation in the following way:

, notice that the notation for y' is changed to

Then you can separate the equation and put the x part of the equation on one side and the y part on the other, like this:

The Next step is to integrate both sides of the equation separately and then simplify the equation.

For the differential equation in question y' + 3x^2 y = 0 the process is:

Step 1: Separate the x part and the y part

Step 2: Integrate both sides

Step 3: Solve the integrals

Simplify the equation:

To solve the Logarithmic expression you have to use the exponential e

Then the solution is:

step-by-step explanation:

compare

so firstly, we need to isolate the y variables to be able to solve these inequalities. firstly, add 0.5x on both sides of the first inequality and subtract 1.5x on both sides of the second inequality:

now since the slope is positive for the first inequality, this means that the line going upwards belongs to the first inequality, and the line going downwards belongs to the second inequality.

next, since y ≥ in the first inequality, this means that the shaded region will be above the first inequality's line, thus shading regions a and b.

next, since y ≤ in the second inequality, this means that the shaded region is going to be below this line, thus shading regions a and c.

since both lines shade region a, this means that region a is the solution.

step-by-step explanation:

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