Solve the differential equation dy/dx = 6xy^2 given that y=1 when x=2.
This equation can be solved using separation of variables. Firstly we rearrange the equation so that all of the y's are on the left hand side and all of the x's are on the right: 1/y2* dy = 6x * dx. Then we integrate both sides to get the following equation: -1/y = 3x2+C. To find the value of C, we plug y=1 and x=2 into the equation and solve it: -1/1 = 3*22+C => C = -13.If we rearrange the equation for y then the final answer is y=1/(13-3x2).
WS
Related Maths A Level answers
All answers ▸Question shown in the answer section as a hyperlinked link.
Use the substitution u=2+ln(t) to find the exact value of the antiderivative of 1/(t(2+ln(t))^2)dt between e and 1.
How to differentiate tan(x)?
Find the gradient of the tangent and the normal to the curve f(x)= 4x^3 - 7x - 10 at the point (2, 8)