Find the solution of the differential equation that satisfies the given initial condition. y' tan x = 3a + y, y(π/3) = 3a, 0 < ; x < π/2, where a is a constant.
1 answer:
Answer:
Step-by-step explanation:
We have a separable equation, first let's rewrite the equation as:
But:
So:
Multiplying both sides by dx and dividing both sides by 3a+y:
Integrating both sides:
Evaluating the integrals:
Where C1 is an arbitrary constant.
Solving for y:
So:
Finally, let's evaluate the initial condition in order to find C1:
Solving for C1:
Therefore:
You might be interested in
Answer: <em>1 </em>
Step-by-step explanation:
<em>4b-5a</em>
<em>4(4)-5(3)</em>
<em>16-5(3)</em>
<em>16-15</em>
<em>1</em>
7 because if the number closest to the number you are rounding is 5 or more you round up otherwise it stays the same
A "regular quadrilateral" is a square, so the length and width are both 4 cm. The surface area of a rectangular prism is given by S = 2(LW +H(L +W)) S = 2((4 cm)*(4 cm) +(6 cm)*(4 cm +4 cm)) S = 2(16 cm² +48 cm²) S = 2*64 cm² = 128 cm² The surface area of the prism is 128 cm².