The solution of dy/dx = −4y with y(0) = 1 is
Answer and explanation
Correct answer: C. y = e^(−4x)
- Step 1: This is separable: dy/y = −4 dx, so ln y = −4x + C. Step 2. With y(0) = 1 the solution is y = e^(−4x). Answer: y = e^(−4x). Why not the others: y = e^(4x) is what you get if you get the sign of the exponent wrong. y = 1 − 4x is what you get if you assume a linear solution. y = e^(−x/4) is what you get if you invert the coefficient.
Practise more Linear algebra, calculus and probability.
Free questions with an explanation for every one, and full timed GATE mock tests.
More Linear algebra, calculus and probability questions
- What is the rank of the matrix with rows (3, 6, 9); (6, 12, 18); (9, 18, 27)?
- If P(A and B) = 0.05 and P(B) = 0.5, what is P(A given B)?
- Find the divergence of F = (x², y², z²) at the point (1, 2, 2).
- The solution of dy/dx = −6y with y(0) = 6 is
- How many labelled spanning trees does the complete graph K7 have?
- How many functions are there from a set of 5 elements to a set of 6 elements?