Question

find the value of y(1) by solving the differential equation y dy/dx=6x²+5,y(0)=2​

Answer 1

Step-by-step explanation:

$y \frac{dy}{dx} = 6 {x}^{2} + 5 \\ ydy = (6 {x}^{2} + 5)dx \\ intigrate \: on \: bth \: sides \: we \: get \\ \frac{ {y}^{2} }{2} = 2 {x}^{3} + 5x \\ {y}^{2} = 4 {x}^{3} +5x \\ taking \: square \: root \: in \: both \: sides \\ y = \sqrt{4 {x}^{3} + 5x } \\ \: at \: x = 1 \\ y = \sqrt{4 {(1)}^{3} + 5(1)} \\ y = \sqrt{9} \\ y = 3$

which is required answer