What is the solution to the equation dy/dx = y^2? (2022)
Practice Questions
Q1
What is the solution to the equation dy/dx = y^2? (2022)
y = 1/(C - x)
y = C/(x - 1)
y = Cx^2
y = ln(Cx)
Questions & Step-by-Step Solutions
What is the solution to the equation dy/dx = y^2? (2022)
Step 1: Recognize that the equation dy/dx = y^2 is a separable differential equation. This means we can separate the variables y and x.
Step 2: Rewrite the equation to separate the variables. Move all terms involving y to one side and all terms involving x to the other side: dy/y^2 = dx.
Step 3: Integrate both sides. The left side becomes ∫(1/y^2) dy and the right side becomes ∫ dx.
Step 4: Calculate the integrals. The left side gives -1/y and the right side gives x + C, where C is the constant of integration.
Step 5: Set the two sides equal to each other: -1/y = x + C.
Step 6: Solve for y. Rearranging gives y = -1/(x + C). To match the form in the short solution, we can rewrite it as y = 1/(C - x).
