solve the differential equation dy/dx = 6xy^2 given that y = 1 when x = 2
First step is to seperate the variables (EQ1) : (1/y^2) dy = 6x Then we integrate each side seperately giving us (EQ2) : -1/y = 3x^2 + C (remembering to add 1 to the power and divide by the new power) subbing in the values for y (1) and x (2) we get - 1 = 12 + C. Therefore C = -13. Subbing this back into EQ2 and rearranging for y we get y = -1/(3x^2 - 13)
DM
Related Maths A Level answers
All answers ▸Write 5cos(theta) – 2sin(theta) in the form Rcos(theta + alpha), where R and alpha are constants, R > 0 and 0 <=alpha < 2 π Give the exact value of R and give the value of alpha in radians to 3 decimal places.
What is integration?
Calculate the integral of e^x*sin x
How do I differentiate: (3x + 7)^2?