Pregunta: 3- Exact differential equations Problems: * Solve the following differential equations, 1) (4.x+3y2 + cos x)dx +(6xy + 2)dy = 0. Ans.: x* + sin x + 3xy² + 2y =C. 2) (sin x + x cos x + cosh(x + 2y)]dx + [3y2 + 2 cosh(x + 2y)]dy=0. Ans.: x sin x + y^+ sinh(x+2y)=C. 3.x? 3) dx+ +6y)dy = 0. Ans.: Vx + y2 +3y=C. 21.r + y2 + x + y 4) + 2x sinh y?)dx+(In x +

3- Exact differential equations Problems: * Solve the following differential equations, 1) (4.x+3y2 + cos x)dx +(6xy + 2)dy = 0. Ans.: x* + sin x + 3xy² + 2y =C. 2) (sin x + x cos x + cosh(x + 2y)]dx + [3y2 + 2 cosh(x + 2y)]dy=0. Ans.: x sin x + y^+ sinh(x+2y)=C. 3.x? 3) dx+ +6y)dy = 0. Ans.: Vx + y2 +3y=C. 21.r + y2 + x + y 4) + 2x sinh y?)dx+(In x + 2x’ycosh y?)dy=0. Ans.: yIn x + x² sinh y2 =C. X 2x 6) y' 2x2 6.xy x? 5) - +2)dx -dy=0. Ans.: +2x = C. 2x + 3y? (2x + 3y?)? (2x + 3y) 2x+3y2 +4r Ans.: y3 - r* = eth? +C. 3y2 - 2xyet' 7) (y? - +2)dx+-+-+2y(x+1)]dy=0. x(x + y) x+y Ans.: (x+1)y? + In(x + y) + 2x - Inx=C. 8) (sin” y + cos²x) dy tan y.sin 2x. Ans.: sinº y +3cos” x.sin y=C. dx 9) 2y sin ydy-(1-сos y)dx - x(csc y-cot y)dy=0. Ans.: y² + xcot y =C. .X sin y 10) (y+e-e)dx + (1+e)dy=0. e Ans.: e**) + ye' - x=C.