<span>−12x3y5 − 9x2y2 + 12xy3</span>
-3xy^2(4x^2y^3+3x-4y)
me so sorry come back laterAnswer:
Step-by-step explanation:me so sorry come back later
Answer:
Step-by-step explanation:
Slope of line A = 
= 
= 3
Slope of line B = 
= 
Slope of line C = 
= 
5). Slope of the hypotenuse of the right triangle = 
= 
= 
Since slopes of line C and the hypotenuse are same, right triangle may lie on line C.
6). Slope of the hypotenuse = 
= 3
Therefore, this triangle may lie on the line A.
7). Slope of hypotenuse = 
= 
Given triangle may lie on the line C.
8). Slope of hypotenuse = 
= 
Given triangle may lie on the line B.
9). Slope of hypotenuse = 
= 
Given triangle may lie on the line B.
10). Slope of hypotenuse = 
= 3
Given triangle may lie on the line A.
Answer:
a solution is 1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Step-by-step explanation:
for the equation
(1 + x⁴) dy + x*(1 + 4y²) dx = 0
(1 + x⁴) dy = - x*(1 + 4y²) dx
[1/(1 + 4y²)] dy = [-x/(1 + x⁴)] dx
∫[1/(1 + 4y²)] dy = ∫[-x/(1 + x⁴)] dx
now to solve each integral
I₁= ∫[1/(1 + 4y²)] dy = 1/2 *tan⁻¹ (2*y) + C₁
I₂= ∫[-x/(1 + x⁴)] dx
for u= x² → du=x*dx
I₂= ∫[-x/(1 + x⁴)] dx = -∫[1/(1 + u² )] du = - tan⁻¹ (u) +C₂ = - tan⁻¹ (x²) +C₂
then
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) +C
for y(x=1) = 0
1/2 *tan⁻¹ (2*0) = - tan⁻¹ (1²) +C
since tan⁻¹ (1²) for π/4+ π*N and tan⁻¹ (0) for π*N , we will choose for simplicity N=0 . hen an explicit solution would be
1/2 * 0 = - π/4 + C
C= π/4
therefore
1/2 *tan⁻¹ (2*y) = - tan⁻¹ (x²) + π/4
Working attached below:
Hope this helps! Any questions let me know :)