Please help me solve this differential equation : x^3+ ¡¼(y+1)¡½^(2) dy/dx=0
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Hi, sorry, the differential equation is:
x^3+(y+1)^2 dy/dx=0
To solve the differential equation, let's follow these steps:
Step 1: Separate the variables.
Rearrange the equation so that the variables x and y are on different sides of the equation:
x^3 + ¼(y+1)² dy/dx = 0
Step 2: Multiply through by dx.
Now, multiply both sides of the equation by dx to eliminate the dy/dx term:
x^3 dx + ¼(y+1)² dy = 0
Step 3: Integrate both sides.
Integrate both sides of the equation with respect to their respective variables:
∫x^3 dx + ∫¼(y+1)² dy = ∫0 dx
Integrating x^3 with respect to x:
(x^4)/4 + ∫¼(y+1)² dy = C
Integrating ¼(y+1)² with respect to y:
(x^4)/4 + (y+1)³/12 = C
where C is the constant of integration.
Therefore, the general solution to the differential equation is:
(x^4)/4 + (y+1)³/12 = C