ee 2 cxy + = 4 ec 2x sin 2x cos + + − = y
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Soal PD Linear : 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. y′ − y = 2e x y′ − 2 y = cos 2 x 2 dx − 2 xy = 6 y e y (jawaban dengan fungsi Y) dy dy + y = ex dx dy ( x 2 + 1) + xy = x 2 dx dy = y sin x dx dy + ( y − 2 sin x ) cos x dx = 0 dy x 2 ln x ⋅ + xy = 1 dx dy x 2 + 2 y = dx x dy 4 ln x − 2x 2 y = dx x3 Jawaban: 1. y = 2x ex + c ex 2. y= 3. x = 3y 2 e y + c e y 4. 2y = e x + c e−x 5. ( x − 2 y ) x 2 + 1 = ln (x + x 2 + 1 ) + c 6. y ⋅ e cos x = c 7. y + 2 = 2 sin x + c e − sin x 1 + y ln x = c x y = x 2 (ln x + c ) 8. 9. − cos 2x + sin 2x + c e 2x 4 2 10. x 2 y = 2 ln 2 x + c 2