Ordinary Differensial Equation

1. Tentukan solusi persamaan differensial biasa berikut ini.
1. 𝑥√1 − 𝑦2 𝑑𝑥 + 𝑦√1 − 𝑥2 𝑑𝑦 = 0 𝑦 = 3 ketika 𝑥 = 2
2. 𝑦′
=
2𝑥 𝑦2
+𝑥
𝑥2 𝑦−𝑦
𝑦 = 0 ketika 𝑥 = √2
3. 𝑦𝑑𝑦 + ( 𝑥𝑦2
− 8𝑥) 𝑑𝑥 = 0 𝑦 = 3 ketika 𝑥 = 1
4. ( 𝑥 + 𝑥𝑦) 𝑦′
+ 𝑦 = 0 𝑦 = 1 ketika 𝑥 = 1
5. 𝑦′
+ 𝑦 = 𝑒 𝑥
6. 𝑥2
𝑦′
+ 3𝑥𝑦 = 1
7. 𝑑𝑦 + (2𝑥𝑦 − 𝑥𝑒−𝑥2
)𝑑𝑥 = 0
8. 𝑦′
cos 𝑥 + 𝑦 = 𝑐𝑜𝑠2
𝑥
9. 𝑦′
+
𝑦
√𝑥2+1
=
1
( 𝑥+√𝑥2+1)